All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
It is allowed to make group Dhikr after the prayers in an orderly manner without causing disturbance. This is supported by the narration of Ibn Abbas (may Allah be pleased with him) who said: "Raising the voice with Dhikr when people finish their obligatory prayers was done during the time of the Prophet (peace be upon him)." Ibn Abbas also mentioned, "I knew when they finished [prayer] because I heard it." [Transmitted by Bukhari & Muslim].
Sheikh al-Islam al-Nawawi (may Allah have mercy on him) mentioned in his commentary on Sahih Muslim (Vol.5/P.84): "This is evidence for what some of the scholars from among As-Salaf As-Saleh(Righteous predecessors) said, that it is recommended to raise the voice with Takbeer (Saying Allahu Akbar) and Dhikr (Remembrance of Allah) after the obligatory prayers. Among those who recommended this, from among the later scholars, is Ibn Hazm al-Zahiri."
Sheikh al-Islam Ibn Hajar al-Haytami (may Allah have mercy on him) narrated in his book "Al-Fatawa al-Fiqhiyya al-Kubra, Vol.1/P.158" from al-Mutawalli, one of the scholars of the Shafi'i school, and others, the recommendation for the congregation to always raise the voice with Dhikr, based on the apparent meaning of the earlier hadith narrated by Ibn Abbas.
He (may Allah have mercy on him) also said in "Al-Fatawa al-Hadithiyya, P.55": "The devotional practices (awrad) of the Sufis that they recite after the prayers, according to their customary behavior, have a sound basis. Al-Bayhaqi narrated from Anas (may Allah be pleased with him) that the Prophet (peace be upon him) said: 'To remember Allah The Almighty with a group after the Fajr prayer until sunrise is dearer to me than the world and all it contains, and to remember Allah The Almighty with a group after the Asr prayer until sunset is dearer to me than the world and all it contains.' Abu Dawood also narrated from him that he (peace be upon him) said: 'To sit with a group who are remembering Allah The Almighty from the Asr prayer until sunset is dearer to me than freeing four slaves from among the descendants of Isma'il, and to sit with a group who are remembering Allah The Almighty from the Fajr prayer until sunrise is dearer to me than freeing four slaves.' Ahmad and Muslim also narrated that he (peace be upon him) said: 'A group that remembers Allah does not gather without being surrounded by angels, covered by mercy, bestowed with tranquility, and mentioned by Allah among those with Him.' If it is established that what the Sufis customarily do, gathering for Dhikr and awrad after Fajr and at other times, has a sound basis in the Sunnah, as we have mentioned, then there is no objection to them in that."
Moreover, Al-Buhuti, may Allah have mercy on him, mentioned in his book "Kashaf al-Qina'an Matn al-Iqna, Vol.2/P.388" that some scholars of the Hanbali school recommended raising one's voice with Dhikr (Remembrance of Allah) after the prayer.
As for saying the Tahleel (La ilaha illallah……..) ten times after the prayer, this is mentioned after the Fajr and Maghrib prayers. This is narrated in a hadith from Abu Dharr, may Allah be pleased with him, that the Prophet Mohammad (peace be upon him) said: "Whoever says, after the Fajr prayer while still sitting in his place, before speaking: 'La ilaha illallah wahdahu la sharika lahu, lahul-mulku wa lahul-hamdu yuhyi wa yumitu wa huwa 'ala kulli shay'in qadir' ten times, ten good deeds will be recorded for him, ten sins will be forgiven, and he will be elevated ten degrees. He will be protected from every disliked thing throughout that day, and he will be guarded against the devil, and no sin will be attributed to him for that day except associating partners with Allah (shirk)." [Narrated by At-Tirmidhi, who said: This is a good and authentic hadith but strange in its chain of narrators]. Some narrations also mention it after the Maghrib prayer.
Some may differ regarding what the Shafi'i school of thought holds, which is that the recommended supplications (Adhkar) after prayers, whether it's the Tahleel, Takbeer, or Tasbeeh (Saying SubhanaAllah), should be done quietly and not loudly. They do not consider it recommended to recite them loudly except for the Imam sometimes, to teach people these supplications. In that case, it is permissible to recite them loudly for the purpose of teaching, and once the teaching is achieved, one should return to the recommended practice of reciting them quietly as per the Sunnah.
It is mentioned in the Shafi book entitled [Explanation of Al-Muqaddimah Al-Hadramiyyah/page 245]: "Every worshipper should silently recite Dhikr and make Dua, except for the Imam who intends to teach the present congregation... he should recite aloud, meaning both Dhikr and Dua, until they learn, then he should recite silently. This is the position adopted by Imam Shafi'i and his companions regarding the hadiths about reciting aloud."
The answer to this issue is that nowadays, mosques usually have new worshippers who may not have learned the rulings of the recommended Dhikr after prayer. Therefore, there is no harm for the Imam to recite the Dhikr aloud after every prayer to teach the people.
It is worth noting that the narration attributed to Ibn Mas'ud, may Allah be pleased with him, regarding the prohibition of raising the voice with Dhikr has not been authentically attributed to him. Ibn Hajar al-Haytami, may Allah have mercy on him, mentioned in his book "Al-Fatawa Al-Fiqhiyya Al-Kubra, Vol.1/P.177" that what is reported from Ibn Mas'ud about seeing people raising their voices with Dhikr in the mosque and saying, "I see you as nothing but innovators," until he expelled them from the mosque, is not authentic and has not been confirmed."
In conclusion, there is no objection to those who raise their voices with Dhikr, nor to those who do so quietly. This is since each of them has their evidence and justification. And Allah The Almighty knows best.